Distortion correction



' Nov. 4, 1958 R. w. KETCHLEDGE DIsToRTIoN CORRECTIGN 2 Sheets-Sheet 2F/G. /4

Filed sept. 4,1953

/NVENTOR R. W KETCHLEDGE ATTORNEY DISTGRTION CORRECTION Raymond W.Ketchledge, Whippany, N. J., assignor to Beil Telephone Laboratories,Incorporated, New viforir, N. Y., a corporation of New York ApplicationSeptember 4, i953, Serial No. 378,530

17 Claims (Cl. S33- 28) This invention relates to vsignal transmissionsystems and particularly to means for correcting or equalizingimperfections in the gain and phase or delay of such transmissionsystems.

An object of the invention is to provide data for equalization in such aform as to avoid trial and error adjustment of equalizers.`

A second object is to make equalizer adjustment more rapid and accurate.

A third object is to permit simple adjustment of equalizers havingshapes chosen without restrictions.

Signal transmission systems, particularly those which transmit a widefrequency band over a considerable distance, suffer from transmissionimperfections. These irnperfections arise from the inability of thesystem designer to construct amplifying devices andiixed equalizerswhich exactly correct for the variations in the attenuation and phase,or delay, characteristics of the system. Furthermore, transmissionthrough the system may be variable due to aging, temperature changes, orother reasons. Therefore, it is necessary to provide the system withadjustable equalizing networks ,which can be so adjusted as to removethe bulk of the transmission imperfections. Typical loss correctingnetworks of this type are described, for example, in a paper entitledVariable Equalizers, by H. W. Bode, in the Bell System TechnicalJournal, April 1938.

Equalizers introduce shapes which, in general, interact in the sensethat each of several shapes may control the transmission of a particularfrequency. By shapeis meant the change in the attenuation or delay ofthenetwork as a function of frequency. Thus, it is dicult to determinethe best setting of the various equalizer shapes since many combinationsof settings will yield good equalization atra particular frequency.

Ithas., therefore, become a common practice to use shapesfwhich-interact as little as possible in the sense of frequency overlap of theshapes. While this eases the adjustment problem by vmaking thetransmission of a particular frequency primarily dependent upon aparticular equalizer control or shape, it also tends to degradeperformance because broad overlapping shapes generally yield a moreaccurate equalization. Thus, one object of the present invention is toremove the restrictions on the choice of practical equalizer shapes.

In thepast, -manual equalizers have been adjusted'by taking the systemout of service, measuring its transmission, adjusting the equalizers,remeasuring the transmissionreadjusting, and continuing the processuntil the desired transmission is obtained. For a complex equalizer withmany controls, this takes considerable time because of thetrial-and-error nature of the process. On the other hand, the presentinvention permits the-direct determination of the required equalizeradjustments and thereby eliminates trial and error.

Inaccordance with one embodiment of the invention, an adjustable`attenuation or delay equalizer and one or more suitable weightingnetworks are associated with` the Y 2,859,413 Patented Nov. 4, 195,8

2...: transmission line to be equalized, a suitable mnltiplefrequencysignal is applied to the combination, and the change in the averagetransmission caused by therinsertion of the weighting network isdetermined. The change lthus found is proportional to the requiredequalizer adjustment. The equalizer may havecne or more adjustableshapes. These shapesl are unrestrictedas top'form Vbutinayadvantageously be orthogonally related. The applied 'signal may beobtained Vfrom a,constant-levelsource of a periodic sweep-frequency orother multiple-,frequency v oltage which covers the range to beequalized. The received signal is passed through one or more detectorsand displayed on a voltmeter the reading of which `is indicative of thedirection and amount of the adjustment to be made in the equalizer shapeto equalize the transmission line. Alternatively, the voltmeter readingmay be recorded for future use or the voltage may be applied directly toa control element of the equalizerto effect an automatic adjustment. Ifthe equalizer has more than one adjustable shape, one or more ditferentweighting networks are substituted, foreach of the shapes, and theshapes are adjusted one at a time. If the equalizer `shapes areorthogonally related, no weighting networks are `required but they maybe used for added accuracy.

i The adjustment of each shape is independent ofthe ladjustmentof theother shapes,.soy that no readjustmentis necessary. A predistorter maybe associated with vthe line if a transmission characteristic otherthanflat-is desired. Also, in some cases it is desirable to inludein theline a wave lter which will transmit only the "frequency range to beequalized.

The nature of the invention and its various objects,

features, and advantages will appear more fully in the followingdetailed description of preferred v embodiments illustrated in theaccompanyingdrawings, of which Fig. l is a block diagram of an adjustingcircuit in accordance with -theinvention fonusewith -eitherattenuationor delay equalizers;

Fig. 2 is a schematic circuit, partly in block,o` f a sweep type ofmultiple-frequency,source suitable for use in the circuit of Fig. l;

Fig. 3 is the voltage versus time characteristic of a triangular wavegenerator suitablefor use ,inI the, circuit of Fig. 2;

Fig. 4 is a schematic circuit of a warping network suitable for use inthe circuit ofFig. 2;

Fig. 5 is a typical output voltage versus frequency characteristic ofthe warping network shown in Fig. 4.

Fig. 6 vis a schematic circuit, partly in block, of a yfrequencymodulator suitable for use in .the sweep-source circuit shown in Fig. 2;I

Figs. 7 and 8 show the circuits, respectively, of va plus 'and a minusattenuation detector suitable-for use inthe circuit of Fig. 1;

Fig. 9 shows, partly in block, a delay detector suitable for use in thecircuit of Fig. l;

Fig. l0 shows three harmonically related cosine shapes suitable for theequalizer shown in Fig. l;

Fig.'1l shows a pair of overlapping, orthogonal, nonharmonic equalizershapes;

Fig. 12 shows three non-overlapping, orthogonal, equall izer shapes;

Fig. 13 shows three overlapping, non-orthogonal equalizer shapes;

Fig. 14 presents graphs of the phase of the fundamental versus frequencyfor equalizer shapes which arecosine cuives on linear or warpedfrequency scales, respectively; an

Fig. l5 shows frequency versus time characteristics for linear andwarped scanning, respectively.

By way of introduction, some of the theory underlying the invention willbe presented. Consider a translent to 'the solution of simultaneousequations.

3 mission system provided with a total of N adjustable equalizer shapes.Assume for the moment that the transmission error of the system consistssolely of a shape which is alinear combination of the shapes availablein the equalizer. There exists, therefore, a setting for each vequalizershape which, in combination with the others,

completely corrects for the transmission error. The re- ,quired settingscan be determined by trial and error, but

this inefficient process can be avoided by a process equiva- Theseequations are developed on the basis that the sum of the requiredindividual equalizer shapes must equal the total system error at allfrequencies. In an actual case Where the system error cannot beperfectly corrected using the available equalizer shapes, an exactcorrection can be vobtained only at a limited number of frequencies, and

there will be small errors at the frequencies between the Ymatch points.

The determination of the required adjustments when one is given a set ofequalizer shapes and given a system equalization error may be expressedas follows:

Let the equalizer shapes be given by functions of the form To obtain amatch of Smal to the given equalization error, Sgiven, at M frequenciesfrom m=1 to m=M, requires that Stotal given (3) at each frequency fromf1 to M. Or, in terms of Equation 2,

Y Y ft=N again, at each frequency from f1 to fm.

Thus, it is clear that a computational operation equivalent to thesolution of simultaneous equations can be used to determine the properequalizer adjustment. The

present invention, however, accomplishes this result on a continuousrather than discontinuous frequency scale. The match points are,therefore, not arbitrarily selected frequencies.

One can postulate the existence of a weighting function GU) which, whenmultiplied by the equalization error Swen, will give an indication ofthe required adjustment of a particular equalizer shape. Since both Sand G are functions of frequency, their product is also a function offrequency. Therefore, an averaging process is required to obtain thevalue of kn, which is the amount of the shape to be introduced. If thisaveraging process is indicated by a superscript bar, we may write theexpression Sglven :kn (5) where the subscript u denotes the particularweighting function. To show that such afamily G(f) exists, con- '4 sidera case where Equation 3 is rigorously true, that s, where the total ofthe equalizer shapes introduced exactly compensates for the equalizationerror. Then Smal may be substituted for Sgwen in Equation 5 and theresulting value of kn substituted in Equation 2 to obtain the expression1L=N Stmxtf):stututGufWf) (5) It can be shown from Equation 6 that, whenu equals n,

when n does not equal u. equalizer functions,

Expressed in terms of the Fn(f)Gu() =0 (9) when n does not equal u.

From these required relationships, it can be deduced that the Weightingfunction must be so selected that G()Fn(f)=1 (10) when u equals n andG()F(f)=0 (11) when u does not equal n. Y

Equations '10 and l1 show that if the equalization error of the systemis transmitted through a weighting network having a transmissioncharacteristic GuU), the average of the resultant signal will beproportional to kn, the amount of the nth equalizer shape required toequalize the system. It Will be noted that the theory here presentedextends the computational concept from discrete to continuous frequencysampling of the system.

It can be shownthat, for a finite number of given equalizer shapes, manyfamilies of Weighting functions exist. Thus, in general, the Weightingfunctions may be chosen to yield the best type of equalization for theparticular problem at hand. If the equalizer shapes are all members ofan infinite orthogonal set which will compensate the equalization errorperfectly, then any set of weighting function meeting equations 10 andlll for the infinite series is as good as any other. The resultant errorwill be due to the fact that only a finite number of terms are availablein the equalizer. In this case, the equalization solution obtained isthe -adjustment that should be used if an infinite number of terms wereavailable. In complicated cases, the choice of the weighting functionscan often be simplified if one treats the equalizer shapes as members ofan infinite set needed to obtain perfect equalization.

An interesting example of the validity of the concepts outlined hereincan be derived from the established theoryof Fourier analysis. If theequalizer shapes are members of an infinite harmonic set, they areequivalent to the terms of a Fourier series. The shapes are orthogonallyrelated and, if the number is infinite, they are capable of coefficientsA7L or Bn of a Fourier series can be found from the relationships 21r.4f-71; FM) sin nad@ 21r Bfma) @es eds (is) for an even function. Theserelationships describe F(0) for values of @falling between zero and 21r.The Ans and B,',s are the coeiiicients of the sine and the cosine terms,respectively, and correspond to the kns of the equalizer shapes. Thecorrespondence of the integration to an averaging process and Yof sinen@ or cosine n0 to the weighting function is obvious. To nd the ATLcontent ofl F09), we weight 12(0), by sin n0, average (integrate) theirproduct, and thereby get the An sin 11H content of F (0). in general, wetake Sgiventimes Gu, average, and getkn.

To summarize, the equalizer-adjusting procedure in accordance with thepresent invention comprises the following steps: A suitablemultiple-frequency signal covering the entire frequency range to beequalized is transmitted through the combination of line and associatedadjustable equalizer, the resultant transmission is multiplied Yat eachfrequency `by an appropriate weighting functionby means of a suitablenetwork inserted into the signal path, and the change in the averagetransmission due to the insertion of the weighting network is observed.Thisobserved change in transmission is proportional to Vthe requiredequalizer adjustment. lf the equalizer shapes are orthogonal, no addedweighting networks are=required but they may be included to increasethe` precision of adjustment.

Alternatively, `the-transmission deviation may be transmitted throughthe weighting-averaging circuit to indicatefthereq-uired equalizeradjustment directly, without insertion or removal of networks during themeasurement.

Taking up the figures in greater detail, Fig. l shows the-generalarrangement of. an equalizer-adjusting circuit in 4accordance with theinvention for use with either an attenuation or a delay equalizer. Amultiple-frequency source-1 is connected, by means of the switches 2 and6, throughoneof the two parallel branches 3 and 4 to a signaltransmission line or other circuit 7 to be equalized. Included intheline 7 are a wave filter 5 and an adjustable attenuation or delayequalizer 8. A weighting-averaging circuit .l0 is connected to the otherend of the line` 7. The equalizer 8 is ordinarily located at thereceiving end of the lineso that the equalizer` may conveniently beadjusted in accordance with the indication obtained from the circuit 1b.The upper branch 3 includes an attenuation predistorter 11. The lowerbranch 4 includes a balancedv modulator 12. and a delay predistorter13-connected in'tandem. When the equalizer 8 is an attenuationequalizer, the switches 2 and 6 are thrown to the upper position,.asshown, so that the source 1 is connected to the line 7 via the upperbranch 3. When the equalizer S is a delay equalizer, the switches arethrown to the lower position so that the lower branch 4 is in circuit.

The function of the source 1 is to provide at the terminals'14, 1.5 avoltage whichv is constant in amplitude but varies in frequency in aprescribed manner over the frequency range to -be equalized. Thislvoltage may sweep the range or it may be a series of discretefrequencies generated either simultaneously or sequentially. However, inthe particular embodiment shown in Fig. l, a sweep-frequency source ispreferred. A suitable circuit is shown inFig. 2.

As shown in Fig- 2, the sweep .Source .1 .is a netwcrk of the feedbacktype, comprising a principalor mu. ci r cuit 17 and a feedback orbetacircuit 18. The mu circuit 17 includes an amplifier 19 followed by afrequency modulator 20. The beta circuit 18 comprises a warping network22, a rectifier 23, and a load resistor 24grounded at one end. Thevoltage of the triangular waveV generator 27 and that across the loadresistor 24 are nearly equal but of opposite sign. These voltages areadded algebraically by the resistance network l25, 28 and delivered tothe amplifier i9. The amplifier 19 vapplies the difference of thesevoltages to the frequencymodulator '2.0. Thus, through'the feedbackaction lin the beta circuit 18, the output frequency on the terminals14, 1S is related in a desired manner to the voltage from the generator27 by the warping network V22, which determines the relative amount oftime the sweep-frequency signalspends rin the vicinity of a givenfrequency. The amountA and nature of the desired warping of thefrequency-time relationship depends upon the shapes-'provided b yf-theequalizer 8 and will be discussed in greater detail hereinafter.

Fig. 3, which is a plot of voltage versus time, shows a suitable outputwave for the triangular wave generator 27. The voltage rises linearlyfrom zero at thetime t0 to a maximum value VM at the time t1,decreaseslinearly to zero at the time t2, and then repeats the cyclecontinuously. ln certain, but not all, cases it is useful to place t1midway between t0 and t2.

Fig. 4 shows a circuit suitable for the warping network 22 of Fig. 2.The networkhas a pair lof input terminals 29, 3i? and a pair of outputterminals 31, 32 which correspond, respectively, to the similarlynumbered terminals shown in Fig. 2. The circuit comprises a seriescapacitor 35 between'the terminals 29, 31 and a shunt branch constitutedby the series combination of a resistor 36 and an inductor 37 connectedbetween the output terminals 31, 32. The values of the elements 35, i3d,37 are so chosen that, for a constant input voltage on the terminals 29,34B, the output voltage onthe terminals 31, 32 has the frequencyresponse shown by the curve of Fig. 5. Over a band of frequenciesextending, in this case, from zero to fo the characteristic falls fromzero to a maximum negative value of VM', which is approximately equal tothe maximum value VM of the output voltage from the triangular wavegenerator 27, shownin Fig. 3. The output voltage is shown as negative inFig. 5 to stress the fact that the alternating-current output from thenetwork 22 is applied to the rectier 23k to produce across the loadresistor 24 a direct-current voltage whose polarity is opposite to thatof the generator 27. As eX- plained below, the warping network 22 may beomitted in some cases.

Fig. 6 shows a suitable circuit for the frequency modulator 20 of Fig.2. rlhe input terminals 39, 4i) and the output terminals 41, 42correspond to the similarly designated terminals in Fig. 2. The functionof the frequency modulator 20 is to convert the voltage versus timecharacteristic received from the amplifier 19 into a frequency versustime characteristic of the type shown in Fig. l5. As shown, the circuitcomprises an oscillator tube 44, a reactance tube 45, a modulator 46,and a lter 47 The input voltage is impressed upon the gridcathodecircuit of the tube 45 through a choke coil 49. The plate-cathodecircuit of the tube 45 is shunted across the tun'ed circuit of theoscillator tube 44. The reactance tube 45 thus converts a voltage on theinput terminals 39, 40 into a reactance which controls thefrequency ofthe `oscillator tube 44. The operation of this type of circuit isdescribed in greater detail in RadiopEngineers Handbook, by F. E.Terman, first edition, 19.43, pages 654 and 655. The output of the tube44 is fed through the coupled coils 50 to the modulator 46, which isdriven by a fixed-frequency oscillator 51. The combination of thevariable-frequency oscillator comprising thetube 44 andassociatedcomponents, the fixed-frequency oscillator 51, and the modulator 46constitutes a beat-frequency oscillator. The operation of beat-frequencyoscillators is well known' and is described, for example, on pages 507,508 and 509 of the above-mentioned handbook. The modulator 46 may, forexample, be of the copper oxide type, such as is shown in Fig. 24 onpage 553 of the book cited above. The output from the modulator 46 ispassed through the low-pass filter 47, to eliminate the undesiredsidebands, and is available at the output terminals 41, 42. In oneembodiment of the invention which has been successfully operated, thetube 44 oscillates at frequencies ranging between 70 and 80 megacycles,under the control of the reactance tube 45, the oscillator 51 has a xedfrequency of 80 megacycles, the filter 47 cuts off at 25 megacycles, andthe output wave at the terminals 41, 42 is substantially constant inamplitude but varies in frequency cyclically between zero and tenmegacycles.

Returning now to Fig. 1, the predistorter 11 or 13 is required only whenit is desired that the combination of the line 7 and the equalizer 8should have a transmission-frequency characteristic which is other thanfiat or constant. For example, assume that the switches 2 and 6 are inthe positions shown, that the attenuation predistorter 11 has a risingloss-frequency characteristic, and that the attenuation equalizer 8 hasbeen adjusted for a flat over-all transmission characteristic. Then',when the attenuation predistorter 11 is removed, the line 7 and theequalizer 8, in combination, will have a falling loss characteristicwhich is just the inverse of that of the predistorter 11. It issometimes desirable to provide this, or some other, type ofcharacteristic in order to equalize for transmission distortion known'to exist in another part of the system. The delay predistorter 13 may beused to accomplish a similar result when the circuit is used for theequalization of delay.

The function of the balanced modulator 12, in the lower branch 4 whichis used in delay equalization, is to change the instantaneous frequencyof the sweep source 1 into a pair of frequencies having a constantspacing between them. This constant spacing is termed the intervalfrequency. It is well known in the art that such a pair offrequenciesmay be used to determine the delay in a transmission system. Suitablebalanced modulator circuits for generating a double sideban'd wave withcarrier suppressed are shown in Fig. 22 on page 551 of the handbookcited above. In one embodiment, when the output from the sweep source 1varied from zero to ten megacycles, the fixed oscillator 58 had afrequency of 14 kilocycles. 28 kilocycles.

Broadly speaking, the function of the portion of the equalizer-adjustingcircuit to the left of the switch 6, the components of which have beendescribed in some detail above, is to apply to the line 7 through thefilter 5 a signal suitable for use in measuring the output of theequalizer 8. The function of the filter is to limit the signal to thefrequency band to be equalized. it may be omitted if the source 1 isalready so limited. As shown, the equalizer 8, to be described morefully hereinafter, has three independently adjustable control elements53, 54, and 55 shown schematically as variable resistors. It is to beunderstood, however, that the invention is applicableto equalizershaving any number of control elements, including a single one. One sideof the equalizer 8 may be grounded, as shown at 56.

The weighting-averaging circuit 10, to be described in detail below, isconnected across the output of the equalizer 8 between the point 76 andthe ground 56. The output of the circuit is used in determining therequired adjustments of the equalizer control elements 53, 54, and S5 toeffect the desired equalization of the line 7.

To recapitulate, in Fig. l a constant-level sweep frequency from thesource 1 is sent over the upper branch 3, or converted to'a pair ofsweep frequencies in the The resulting interval frequency is then l 8lower branch 4, transmitted through the filter 5, over the line 7, andthrough the equalizer 8,and convertedI in' the circuit 10 todirect-current voltages which are utilized to determine the propersettings for the equalizer 8.

The weighting-averaging circuit 10 comprises three pairs of weightingnetworks 70, 70', 71, 71', and 72,

72', two detectors 73, 74, two resistors 94, 95, a voltmeter 75, andthree switches 77, 78, 79. The switches are ganged together for unitaryoperation as indicated by the broken line connecting them. The networksand the detectors are al1 connected on one side to a common ground, asshown. The switch 77 is connected to the high-side output yof theequalizer 8 at the point 76. The switch 78 is connected to the inputterminal 96 of the detector 73 and the switch 79 to the input terminal98 of the detector 74. The weighting networks are connected in pairs attheir input ends to the contacts associated with the switch 77. Thenetworks 70, 70 are thus connected to the contact 83, the networks 71,71 to the contact 84, and the networks 72, 72 to the contact 85. Attheir output ends the networks 70, 71, and 72 are connected,respectively, to the contacts 87, 88, 89 associated with the switch 78.The networks 70', 71', 72 are similarly connected to the contacts 90,91, and 92 associated with .the switch 79. The output terminals 97, 99of the detectors 73, 74 are connected through the resistors 94, 95,respectively, to the voltmeter 7S.

The detector 73 is indicated as plus (-i) and the detector 74 as minusWhen the circuit is being used for attenuation equalization, the plusdetector 73 may be a diode 101 as shown in Fig. 7. The plate isconnected to the terminal 96 and the cathode to the terminal 97. In Fig.7, the terminals 96 and 97 correspond to the similarly designatedterminals shown in Fig. l. The function of the detector 73 is to convertthe alternating-current signal at the input terminal 96 to a positivedirect-current signal proportional thereto which appears at the outputterminal 97. A similar circuit may be used for the minus detector 74except that the input and output terminals are reversed, `as shown inFig. 8. In Fig. 8, the terminals 98, 99 correspond to the similarlynumbered terminals in Fig. l. The detector 74 converts thealternating-current signal at the input terminal 98 to a proportionalnegative direct-current signal at the output terminal 99.

When delay rather than attenuation is to be equalized, the equalizer 8is a delay equalizer and the detectors 73 and 74 are adapted to detectdelay. In this case, a suitable circuit for the plus detector 73 isshown in Fig. 9, where the input terminal 96 and the output terminal 9 7correspond to the similarly designated terminals in Fig. 1. The delaydetector shown in Fig. 9 comprises a diode 102, a resistor 103, two waveiilters 104, 105, and a phasesensitive rectifier 106. The plate of thediode 102 is connected to the input terminal 96. The resistor 103 isconnected between the cathode and ground to constitute the load. Theoutput ofthe diode 102 is connected in parallel to the input ends of thefilters 104 and 105. The outputs of these filters are connected to thephase-sensitive rectifier 106, a suitable circuit for which isdisclosed, for example, in my Patent 2,434,273, issued January 13, 1948.The input signals at the terminal 96 are rectified by the diode 102 toproduce across the load resistor 103 the difference frequency generatedby the modulator 12 of Fig. 1. This difference frequency is phasemodulated by the delay characteristic of the line 7 and the delayequalizer 8. This characteristic is repeated in a period t2, as shown inFig. 3. rlhus, the signal on the resistor 103 comprises a carrier andvarious sidebands spaced at l/ t1 or l/tz intervals. The filter 105 hasa narrow band which excludes the sidebands but transmits to therectifier 106 a carrier wave of constant amplitude and phase. The filter104, however, has a band wide enough to transmit all of the importantsidebands to the rectiiier 106. The output of the phase-sensitiverectifier-106, appearing at the terminal 97, is a positivedirect-current voltage which is a measure of the deviations fromconstant delay. The circuit shown in Fig. 9 may also be used for theminus detector 74, except that the output polarity of the rectier 106 isreversed so that there is delivered to the output terminal 99, Fig. 1, anegative direct-current voltage which is also a measure of thedeviations from constant delay.

In Fig. l, the resistors 94 and 95 are normally equal. They have valuessuiciently large to prevent troublesome interaction between thedetectors 73 and 74. The voltmeter 75 is preferably of the type havingits zero at the center of the scale.

The operation of one embodiment of the equalizeradjusting circuit inaccordance with the invention will now be described. It will be assumedthat the attenuation distortion of the line 7 is to be corrected. Theequalizer 8 will, therefore, be an attenuation equalizer and theswitches 2 and 6 will be thrown to the upper positions, as shown, toconnect the source 1 to the line 7 via the upper path 3 and the lter 5.It will be'further assumed that the switches 77, 78, and 79 are thrownto the upper positions shown in Fig. 1. Thus, the point 76 is connectedthrough the weighting network '7th to the plus detector 73 and throughthe weighting network 7u to the minus detector 74. It is also assumedthat the networks 7d and 70' together furnish an appropriate weightingfunction for the equalizer shape controlled by the adjustable element53. For example, the network 70 inayprovide the positive part of theweighting function and the network 7G' the negative part. Therequirement is that the sum of the two network characteristics, onebeing positive and theother negative, add up to the desired weightingfunction. Itis only the fact that the weighting function may have tochange polarity with frequencythat necessitates two networks. Thereading on the voltmeter 75, which is the combined outputs of thedetectors 73 and 74, is an indication of the direction and amount of therequired adjustment of the control 53. A positive reading means that thecontrol 53 should be adjusted in one direction and a-negative readingthat it should-be changed in the opposite direction. The magnitude' ofthe voltage reading corresponds to the amount ofadjustment required`Therefore, the control 53 is moved inthe proper direction until thevoltmeter 75 reads zeroor a minimum. The amount of the equalizer shapeassociated with the control 53 is now properly adjusted.

To find theproper setting for the control elem-ent 54, theswitches 77,78, and 79 are thrown, respectively, to the contacts S4, 83, and 91. Theweighting networks 71 and 71 are'thus substituted for 7d and 7d'. Thenetworks 71 and 71', in combination, provide a weighting functionappropriate for the equalizer shape controlled by the element 54. Now,the control 54 is adjusted until the voltmeter 75 reads zero or aminimum. To adjust the third equalizer shape, the switches 77, 78, and79 are thrown to their extreme lower positions to connect intocircuit-the appropriate weighting networks 72 and 72' and the control 55is adjusted for a zero or minimum reading on the voltmeter 75. if thecharacteristics of the weighting networks are properly related to eachotherand to the equalizer shapes, no readjustrnent will be requiredunless, of course, the attenuation of the line 7 changes. The adjustmentof each shape is substantially independent of the adjustment of theother shapes. Because of thisfeature, the adjustment procedure isconsiderably shortened.

To recapitulate, the source 1 sends a constant-level swept ormultiplerequency signal over the transmission line 7 and through theequalizer 8. At the receiving point 76, the system characteristic, on aunit basis, is l-|-S(f), where unity is the flat transmission and SU) isthe equalization error shape. Between the point 76 and the voltmeter 75,the weighting networks such as 70, 70

-and the detectors '73, -74v introduce acharacteristic G (f), -which maybe positive or negative depending upon'the relative transmissions of thenetworks 70,l 7 0. Bychoosing one of the equalization shapes to'be aflatcharacteristic so that for the other shapes G-(f)=0 (14) the1meterv-48will read S(f)G(f) directly. As shown-by Equation 5, this voltagereading is proportional to the factor kw the amount of the nth equalizershape to'be introduced by the adjustment of a .control such as 53. Ifdat gain is not one of the equalizer shapes, if the shape involved is aflat shape, or if for any other reason'Equation l4isnot satisiied, themeter 75 reads tions G( f) has a value of only one polarity, thefunctions may be provided bythe remaining networks 70, 71, 72. Therequired value of kn is found by connecting the appropriate network 70,71, or 72 into the circuit by means offtfhe switches 77 and 78and'reading the meter 75. If the weighting function'GCf) has both`positive and negativevalues, twometer readings are-.required todetermine vtheproper adjustmentlof eachequalizer shape. One of thenetworks., say '/O, is built to provide a characteristic l-j-G (f.)which 1s positive-k throughout they entire, frequency range. With thenetwork 70 connected into the circuit,

the. rneter 75 reads (l-j-S)(lj-G) which, expanded, is`l-j-.S'j(i`rj-.S`G. Another of the networks, say 71, is designed tohave a characteristic 5:0. The network .71

may, for example, be simply an attenuator. Now, with the network Z1substituted for the network 70, the meter 75 reads l- The differencebetween these two readings is G-j-.SG, the value of k7L required foradjusting one of the equalizer shapes.

A third embodiment of the invention is particularly suited to the casewhere the equalizer shapes are orthogonally related and form adequateweighting functions for their ow-n adjustment. The circuit of Fig. 1 ismodied by the omission of the networks 71, 72, '70', 71', 72', thedetector 74, and theswitch 79. The remaining network 70 may be simply athrough electrical connection. Thus, with the switches 77 and 78 in thepositions shown, the point 76 is connected -directly to the detector 73.v An important` example of this embodiment is where the equalizer shapesform a Fourier series of the type shown in Fig. l0, discussed in greaterdetail below. As Equations 12 and 13 show, the shapes themselves are thesame-as, Vand therefore form, their own weighting functions. Theadjustment procedure is very simple. Each of the equalizer controls' 53,54, and 55 is adjusted, in turn, for a minimum reading on the meter '75.When the. equalizer 8 is correctly adjusted, a change in. eitherdirection of any one-of the controls will increase ther meter reading.

As already pointed out, there is no necessary restriction on the, shapesintroduced by the equalizer 8. As examples, Figs. 10, 11, 12, and 13show four general classes of suitable shapes. Three of these classes areorthogonal. They are first, a Fourier series (Fig. 10), second,overlapping non-harmonic (-Fig. 1l), and third, non-overlapping bumpshapes (Fig. 12). These havethe advantage that no weighting networksyare required. and, therefore, the simple adjusting technique of thethird 1 1 embodiment, described above, may be used. However, if the flatloss of the line 7 is changing rapidly, a more precise adjustment of theequalizer may be obtained if suitable weighting networks are employedand the first or second embodiment is used. rlfhe fourth class ofequalizer shapes are the overlapping, non-orthogonal characteristicsshown in Fig. 13. While these shapes will be discussed only on anattenuation basis, similar relationships apply where the shapes aredelay characteristics. The adjusting technique is equally applicable toeither attenuation or delay equalizers.

lllustrative of a Fourier series, Fig. shows the attenuationcharacteristics of three shapes of a suitable cosine attenuationequalizer over the frequency range to be equalized, from zero to fo. Thecurves 59, 60, and 61 correspond, respectively, to the fundamental andthe rst two harmonic terms. An infinite series of such 'terms is capableof describing any continuous function. However, a finite number of termswill provide sufficiently accurate equalization in most cases. lnpractice, it has been found that terms, that is, 25 equalizer shapes,will give excellent equalization. The flat loss A0 is the characteristicobtained when each of the control elements 53, 54, and 55 is set at thecenter of its adjustable range. As each control is moved off center, aproportional positive or negative amount of the corresponding cosineshape is introduced into the equalizer 8. Each of the equalizer shapes,therefore, has an attenuation characteristic given by S(f) :A04-kn cosn0 (15) where 0 is the phase angle of the fundamental, k is a numericalconstant which depends upon the setting of the control and may be eitherpositive or negative, and n identifies the particular equalizer shape. Asuitable cosine equalizer circuit is disclosed in United States Patent2,348,572, to P. H. Richardson, issued May 9, 1944.

In Fig. l0, the fundamental, curve 59, is shown as a true cosine shapeand, therefore, its phase 6' is linearlyA proportional to the frequencyf, as shown by the brokenline curve 63 in Fig. 14. The broken-line curve65 of Fig. l5 shows a typical frequency-time characteristic of theoutput from the sweep source 1 at the terminals 14, 1S when the warpingnetwork 22 is omitted. The frequency rises linearly from zero at thetime t0 to fo at i1 and then descends linearlyto zero again at t2. Thistype of scanning characteristic is suitable for use with an equalizer 8whose phase-frequency characteristic is linear, as shown by the curve 63of Fig. 14.

In some cases, however, it is found that closer equalization isobtainable if the equalizer shapes are distorted cosine curves. Thephase-frequency characteristic of the fundamental equalizer shape may,for example, be of the form shown by the solid-line curve 64 of Fig. 14,which is concave upward. In this case, it is advantageous, but notalways essential, to warp the frequency scale of the scan, bycompressing it at the low frequencies and stretching it at the highfrequencies, to compensate for the non-linearity of the phase-frequencycharacteristic. This is accomplished by inserting a warping network 22whose voltage-frequency characteristic, as shown in Fig. 5, correspondsto the phase-frequency curve 64 of Fig. 14, to produce a concavedownward scanning characteristic such as shown by the solid-line curve66 of Fig. l5 and thereby make the variation of the phase versus timecharacteristic linear.

When the equalizer 8 has harmonic cosine shapes such as those shown inFig. l0, no weighting networks are required. However, as alreadymentioned, the precision of adjustment may generally be improved byproviding them, This is especially true if the flat loss of thetransmission line is varying rapidly at the time the equalizer is beingadjusted. Appropriate transmission characteristics for the weightingnetworks may, for example, be of the form l-l-cos n@ for the network 70and l-cos n0 12 for the network 70. It will be assumed that thesenetworks have such characteristics and that the line '7 and theequalizer S have, in combination, a characteristic l-j-cn cos rw-j-kmCos m0, where m does not equal n. Then, at the input terminal 96 of thedetector 73 there will be a signal characteristic (l-j-cos 119)(l-j-kncos nH-j-km cos m6) and 4at the input terminal 98 of the detector 74 asignal characteristic (l-cos nt9)(l-jk7L cos n64-km cos m6). Since thescanning by the sweep source 1 makes 0 proportional to time and 0 variesbetween zero and 180 degrees, there will appear at the output terminal97 a direct-current envelope like that at the terminal 96 and at theoutput terminal 99 the negative of the envelope at the terminal 93.Since the average of cos n cos m0 is equal to zero when m does not equaln, the voltmeter 75 reads an average signal which is simply kn, thedesired adjustment factor.

In Fig. ll, the curves 106 and 107 are a representative pair ofoverlapping, non-harmonic, orthogonal, equalizer shapes. By denition,two functions Hx) and f(x) are orthogonal over an interval (a, b) if bfarm-ammo (is) that is, if the integral of the product of the functionsis zero over the interval. Each of the curves is a straight line overthe frequency range from zero to fo. The curve 106 has zero slope andits departure from the constant flat loss Ao may be expressed as k1. Thecurve 107 passes through A0 at the frequency fo/2 and has a positiveslope. lts departure from A0 may be expressed as k2(f-f0/ 2). It will beunderstood that, by adjustment, the curve 106 may be raised or loweredand the curve 107 rotated about a pivot point at jiu/2. If theserelationships are inserted into Equation 16, it is found that the curves106 and 107 are orthogonal over the frequency interval fo. In manypractical cases, it is possible to orthogonalize equalizer shapes bywarping the frequency scale. As already explained, this may beaccomplished by means of the warping network 22 shown in Fig. 2. Asmentioned above, the advantage of orthogonal equalizer shapes is thatthey provide their own weighting functions and no additional weightingnetworks are required. The fact that this is so may be deduced bycomparing Equations l0, l1, and 16. This comparison brings out theimportant point that each weighting function must be orthogonal to allequalizer shapes except the one for which it is the weighting function.

Fig. l2 shows three non-overlapping, bump shapes. These are alsoorthogonal, because at any frequency all the shapes but one are zero.The solid-line curves 113, 114, and show the upper adjustment limits andthe broken-line, mirror-image curves 113', 114', and 11S show,respectively, the lower limits. No added weighting networks are requiredwhen the equalizer 8 has shapes of this type.

To represent the fourth class of equalizer shapes, Fig. 13 shows threeoverlapping, non-orthogonal curves 118, 119, and at their upperadjustment limit. The mirror-image lower adjustment limits are notshown. The curve 119 pivots about the point fp, A0. When the equalizer 8has non-orthogonal shapes, weighting networks must be used. The choiceof weighting functions must be guided by the relationship of the shapesto the transmission distortion shapes expected in the line 7 to beequalized. This choice wil affect the accuracy of equalizationobtainable except in the rare case when the equalizer is capable ofproviding substantially perfect equalization. For example, each of theweighting networks such as 70, 71, and 72 may have a transmissioncharacteristic made up of linear combinations of the shapes 118, 119,and 120. However, the networks would differ from each other in therelative amounts, the polarities, or both, of the component shapesemployed.

It is to be understood that the above-described arrangements areillustrative of the application of the principles of the invention.Numerous other arrangements may be devised by those skilled in the artwithout departing from the spirit and scope of the invention.

What is claimed is:

1. In combination, a transmission path having a transmissioncharacteristic which exhibits undesired frequencydependent distortionover a range of frequencies, an equalizer having an adjustable shapeconnected in the path, a constant-level, multiple-frequency voltagesource covering the range connected to one end of the path, a rstnetwork having a transmission characteristic which is constant withfrequency connected at one end to the other end of the path, a detectorconnected to the other end of the first network, an averaging voltmeterconnected to the output end of the detector, a second network, and meansfor substituting the second for the rst network, the second networkbeing a weighting network having a transmission characteristic such thatthe voltmeter reading duc to the second network, minus the voltmeterreading due to the rst network, indicates the direction and the amountof the adjustment of the equalizer shape required to achieve optimumcorrection of the distortion.

2. The combination in accordance with claim 1 in which said equalizer isadapted to compensate attenuation distortion in said path.

3. The combination in accordance with claim 1 in which said equalizer isadapted to compensate delay distortion in said path.

4. The combination in accordance with claim l which includes anattenuation predistorter connected in said path.

5. The combination in accordance with claim l which includes a delaypredistorter connected in said path.

6. The combination in accordance with claim 1 which includes means forrestricting the transmission through said path to said range.

7. The combination in accordance with claim 1 in which the equalizer hasa second adjustable shape and which includes a third network and meansfor substituting the third for the rst network, the third network beinga weighting network having a transmission characteristic such that thevoltmeter reading due to the third network, minus the voltmeter readingdue to the first network, indicates the direction and the amount of theadjustment of the second equalizer shape required to achieve optimumcorrection of the distortion by the second shape.

8. In combination, a transmission path having a transmissioncharacteristic which exhibits undesired frequencydependent distortionover a range of frequencies, an equalizer having two adjustable shapesconnected in the path, means for impressing upon one end of the path aconstant-level, multiple-frequency voltage covering the range, a rstweighting network connected at one end to the other end of the path, adetector connected to the other end of the network, an averagingvoltmeter connected to the output end of the detector, the networkhaving a transmission characteristicwhich produces a reading on thevoltmeter indicating the direction and the amount of the adjustment ofthe rst of the equalizer shapes required to achieve optimum correctionof the distortion by the rst shape, a second weighting network, andmeans for substituting the second for the rst network, the secondnetwork having a transmission characteristic which produces a reading onthe voltmeter indicating the direction and the amount of the adjustmentof the second of the equalizer shapes required to achieve optimumcorrection of the distortion by the second shape.

9. The combination in accordance with claim 8 in which said equalizer isadapted to compensate attenuation distortion in said path and saiddetector is adapted to detect attenuation.

l0. The combination in accordance with claim 8 in which said equalizeris adapted to compensate delay distortion in said path and said detectoris adapted to detect delay.

1l. The combination in accordance with claim 8 in which said detectorcomprises a diode and a phase-sensitive rectifier connected in tandem, awide-band wave filter interposed therebetween, and a narrow-band wavelter connected between said rectier and said diode.

12. In combination, a transmission path having a transmissioncharacteristic which exhibits undesired distortion over a range offrequencies, an equalizer having two adjustable shapes connected in saidpath, means for impressing upon one end of said path amultiple-frequency Voltage covering said range, a pair of weightingnetworks connected at their input ends in parallel to the other end ofsaid path, a pair of oppositely poled detectors connected at their inputends, respectively, to said networks, a voltmeter connected to theoutput ends of said detectors, said networks having transmissioncharacteristics which in combination produce a reading lon saidvoltmeter which indicates the direction and the amount of the adjustmentof one of said equalizer shapes required to achieve optimum correctionof said distortion by said one shape, a second pair of weightingnetworks, and means for substituting said second pair for said rst pairof networks, said second pair of networks having transmissioncharacteristics which in combination produce a reading on said voltmeterwhich indicates the direction and the amount of the adjustment of theother of said equalizer shapes required to achieve optimum correction ofsaid distortion by said other shape.

13. The combination in accordance with claim 12 in which said shapes areoverlapping, non-orthogonal curves.

14. The combination in accordance with claim 12 in which said equalizershapes are orthogonally related over said range.

15. The combination in accordance with claim 14 in which said shapes areharmonically related cosine curves.

16. The combination in accordance with claim 14 in which said shapes areoverlapping non-harmonic curves.

17. The combination in accordance with claim 14 in which said shapes arenon-overlapping curves of the bump type.

References Cited in the le of this patent UNITED STATES PATENTS2,102,138 Strieby Dec. 14, 1937 2,337,541 Burgess Dec. 28, 19432,465,531 Green Mar. 29, 1949 2,625,614 Sebelleng Jan. 13, 19532,753,526 Ketchledge July 3, 1956

